WOW ! 4 kids in a rented RV while dad is cruising along on his motorcycle...........
Sounds like a divorce to me. LOL Or something you could make a movie out of....of wait, they already did that.
Seriously, if there is a way to be serious here, the closest I came to this sceneraio was a few years back, we took a family vacation from TX to AZ so i could drop off my bike at SBC to have a stroker motor built. After dropping it off, we headed to the Grand Canyon for a few days of R&R. Worked out OK, but during the time we were dropping off, picking up, test driving, bullchitting, etc, the family was pretty bored, plus the temp was 118, plus the stroker motor cost way more than the vacation itself. Don't know what age your kids are, but if they can get some seat time in, it might help everyone out. Hope your wife is VERY understanding.
Good luck.